Kinematical higher-twist corrections in $\gamma^* \to M \bar M \gamma$. I. Neutral meson production

We carry out the calculation of kinematical higher-twist corrections to the cross section of $\gamma^* \to M \bar{M} \gamma$ up to twist 4, where $M$ is a scalar or pseudoscalar neutral meson. The three independant helicity amplitudes are presented in terms of the twist-2 generalized distribution amplitudes (GDAs), which are important non-perturbative quantities for understanding the 3D structure of hadrons. Since this process can be measured by BESIII in $e^+ e^-$ collisions, we also perform the numerical estimate of the kinematical higher-twist corrections by using the kinematics of BESIII. We adopt the $\pi \pi$ GDA extracted from Belle measurements and the asymptotic $\pi \pi$ GDA to study the size of the kinematical corrections in the case of pion meson pair, and a model $\eta \eta$ GDA is used to see the impact of target mass corrections $\mathcal O(m^2/s)$ for $\gamma^* \to \eta \eta \gamma$. Our results show that the kinematical higher-twist corrections account for $\sim 20\%$ of the cross sections at BESIII on the average, and it is necessary to include them if one tries to extract GDAs from experimental measurements precisely. Furthermore, the energy-momentum tensor (EMT) form factors can be obtained for mesons with the help of their GDAs, from which one can investigate interesting quantities such as the meson mass radius and mass distribution.